In what seems to be a huge improvement to the original, Destiny 2 according to an article on Wccftech, EDGE magazine and other outlets have reported that Destiny will feature more than 80 PvE activities and story missions. What isn't really clear just yet is how many of it is Story missions and how much of it is just filler (Strikes, Raids, etc). As much as I liked the Original it just feel like it was lacking something and that was a really good story with cutscenes. The narrator telling the story while the game was loading into a mission really seemed to turn me off because that's something you would expect from a earlier age of video games.
Game Rant has reported that there will also be more cutscenes (more than 50 total) so hopefully the story will be much bigger than the 1st game and also more immersive. Considering that there's more than 50 cutscenes and that one destiny developer hoped that "People complain about how long the story is" that assures me that the story won't be lacking at least in content however the determination of how good the story will be is anybody's guess at this point. How big the story is doesn't determine how great it is so don't be fooled, There's an old saying that "quality is better than quantity" so take that as a piece of wisdom.